1. Prepare the Puff Pastry:

• Thaw the puff pastry sheet in the refrigerator until pliable (usually about 30 minutes to an hour). Avoid leaving it out at room temperature for too long, as it can become too soft and difficult to work with.
• Once thawed, gently unfold the pastry and cut it into 9 even squares using a sharp knife or a pizza cutter. Place the squares on a parchment-lined baking sheet, spacing them about 1 inch apart to allow for expansion.

2. Make the Peach Filling:

• Peel, pit, and slice the peaches into thin wedges. Aim for uniform slices (about 1/4 inch thick) for even cooking.
• In a small bowl, combine the peach slices with sugar, cinnamon, vanilla extract, and flour. Toss gently to coat the peaches thoroughly. The flour helps to absorb excess juice and prevents the pastry from becoming soggy.

3. Assemble the Tarts:

• Divide the peach mixture evenly among the pastry squares, placing a small mound in the center of each one. Avoid overfilling to prevent leaks during baking.
• Brush the edges of each pastry square with the beaten egg. This will give the tarts a shiny, golden-brown finish.

4. Bake the Tarts:

• Preheat your oven to 400°F (200°C). Ensure the oven is fully heated before baking for consistent results.
• Bake the tarts on the middle rack for 13-15 minutes, rotating the pan halfway through. Look for puffed edges and a light golden color. Keep a close eye on the tarts during the last few minutes to prevent over-browning.
• Once done, remove the tarts from the oven and allow them to cool on the baking sheet for 5-10 minutes before transferring them to a wire rack.

5. Prepare the Icing:

• In a small bowl, whisk together the powdered sugar, vanilla extract, and milk until smooth. Adjust the thickness by adding more milk (for a thinner drizzle) or more sugar (for a thicker glaze).
• Once the tarts have cooled slightly, drizzle the icing over the tops using a spoon or a piping bag for a polished finish.